Second-generation hemodynamic and amniotic fluid dynamics model

TTTS. Second-generation hemodynamic and amniotic fluid dynamics model

In our second model,5 we added amniotic fluid dynamics to our first model. We had to adapt the mechanism of fetal blood volumetric growth. We included that the growing fetus and amniotic cavity acquire fluid and nutrients from the maternal circulation to maintain the volume of the total body fluid as well as the amniotic fluid. 

Fluid and nutrients are provided by the transplacental fluid flow from the maternal to the fetoplacental circulation, implying 

Because the primary model parameters are the blood volume of the twins, we had to relate blood volume with total body fluid volume. We assumed the fetal blood is a constant fraction of 10% of the total body fluid: 

The growth of anastomoses, placenta and fetuses, the blood volume vs blood pressure curves, the relation for net fetofetal transfusion, and the model input parameters, were all taken identical as in the first model. In eqn (9), TotalBodyFluidGrowth directly follows from eqn (7) as the difference between TransPlacent- Flow and AmnioticFluidGrowth. 

Growth of the amniotic fluid volume is the sum of urine production and lung fluid secretion minus the sum of swallowing and intramembranous flow, the flow from amniotic cavity to the fetal blood across the total surface of the placenta, umbilical cord, and fetal skin. 

The additional parameters included in the second model for each twin are those that control the various fluid flows included in the model. First, the transplacental fluid flow was described by the Starling equation, proportional to the difference between the maternofetal hydrostatic and colloid osmotic pressure (COP) gradients: 

Although the Starling equation is an accepted choice here, for example,2 we acknowledge that transplacental fluid transfer is a complex and still incompletely understood mechanism. Recently, new pathways have been identified which are known to be capable of somehow regulating this fluid transfer.20 The maternal blood COP is assumed to be unaffected by fetofetal transfusion. The first new model parameter then is the fetal blood COP. 

Secondly, we assumed that swallowing (i.e. thirst mediated) is controlled by the fetal blood osmolality, which therefore is the second new parameter. We assumed that swallowing becomes equal to fetal lung fluid secretion once the fetal blood osmolality has decreased by 4% or more of its normal value.5 So, fetal blood osmolality is the third new parameter. Thirdly, the intramembranous flow is also taken as a Starling equation, proportional to the difference between the hydrostatic and osmotic pressure gradients between amniotic fluid and fetal capillaries. 

The osmotic pressure gradient relates to the osmolalities of amniotic fluid and fetal blood. Hence, the amniotic fluid osmolality is the fourth new model parameter. So, our second model comprises 10 growth (differential) equations, 5 for each twin, of (1) fetal blood volume, (2) amniotic fluid volume, (3) fetal blood osmolality, (4) amniotic fluid osmolality, and (5) fetal blood COP (see Table 6.1). 

Furthermore, urine production was controlled by a pressure–diuresis curve, where urination ceases once the pressure decreased to half or less of the normal value, and otherwise increases proportional to the normalized arterial pressure squared. Lung secretion was included as a function of gestation without a control mechanism. The net fetofetal transfusion along the anastomoses links three of the five equations of each twin, not only transfusing blood volume but also blood colloids and osmoles. The equations are solved numerically as before.